How to UV unwrap a circle?
1: Are you following the  “Blender for beginners: Alarm clock 1 of 2” tutorial.    https://www.youtube.com/watch?v=Ay7fgeQC1WI   ?

2: When UV unwrapping the clock face at 11:40 are you saying that you have two circles showing up in the UV space instead of one big one?

Two circles unwrapped instead of one means that you have two circles selected in the 3D edit window before unwrapping.

You need to go back to the 3D edit window and check out why two circles were selected instead of only one.

Perhaps you have the the glass lens selected instead of the clock face?

If you still don't see how two circles are being selected then I suggest you add your .blend file to your post 

https://blend-exchange.giantcowfilms.com/

then someone can take a look at it for you.